Downsizing of COVID-19 contact tracing in highly immune populations

Contact tracing is a key component of successful management of COVID-19. Contacts of infected individuals are asked to quarantine, which can significantly slow down (or prevent) community spread. Contact tracing is particularly effective when infections are detected quickly, when contacts are traced with high probability, when the initial number of cases is low, and when social distancing and border restrictions are in place. However, the magnitude of the individual contribution of these factors in reducing epidemic spread and the impact of population immunity (due to either previous infection or vaccination), in determining contact tracing outputs is not fully understood. We present a delayed differential equation model to investigate how the immunity status and the relaxation of social distancing requirements affect contact tracing practices. We investigate how the minimal contact tracing efficiency required to keep an outbreak under control depends on the contact rate and on the proportion of immune individuals. Additionally, we consider how delays in outbreak detection and increased case importation rates affect the number of contacts to be traced daily. We show that in communities that have reached a certain immunity status, a lower contact tracing efficiency is required to avoid a major outbreak, and delayed outbreak detection and relaxation of border restrictions do not lead to a significantly higher risk of overwhelming contact tracing. We find that investing in testing programs, rather than increasing the contact tracing capacity, has a larger impact in determining whether an outbreak will be controllable. This is because early detection activates contact tracing, which will slow, and eventually reverse exponential growth, while the contact tracing capacity is a threshold that will easily become overwhelmed if exponential growth is not curbed. Finally, we evaluate quarantine effectiveness in relation to the immunity status of the population and for different viral variants. We show that quarantine effectiveness decreases with increasing proportion of immune individuals, and increases in the presence of more transmissible variants. These results suggest that a cost-effective approach is to establish different quarantine rules for immune and nonimmune individuals, where rules should depend on viral transmissibility after vaccination or infection. Altogether, our study provides quantitative information for contact tracing downsizing in vaccinated populations or in populations that have already experienced large community outbreaks, to guide COVID-19 exit strategies.

2 Major Remarks 1. The title of the paper and the discussion suggest that the downsizing of contact tracing occurs simultaneously to the roll-out in of the vaccine and lifting of contact restrictions. Contrasting this, the paper deals with the situation where a fixed amount of the population is already vaccinated, contacts remain constant and contact tracing is only implemented after the fact. This should be formulated more explicitly in the title as well as introduction and discussion section of the paper.
2. The conclusion after Equation (17), namely that q * is always smaller than 1 is mistaken. Indeed, take p c very small, then the right-hand-side of Equation (17) blows up. Additionally for q * to be known analytically one would have to calculate the time-varying probabilities p Ic , p Ip , p Ia which, to my knowledge, one cannot. The authors should thus formulate this more carefully in the discussion section of the paper, especially the sentence "Analogously, we show that, when highly efficient, contact tracing alone can be considered an effective control measure even in the absence of vaccination or social distancing".
3. While some of the parameters in Table 1 stem from references, others are based on estimates or choice of the authors, e.g. the total population size N , the probability of infection given a contact α, the contact rate c and the amount of imported cases m. Indeed, a back-of-the-envelope calculation (setting q to 0) yields which seems more in line with the Delta variant than the original strain.
The text should elaborate more on the reasons for these specific values, ideally citing studies (especially for the critical parameters α and c).
4. The contact tracing efficiency q is never formally introduced and differs in meaning across the paper; in Equation (5) it is meant as the fraction of symptomatic cases whose contacts are traced while in Section 4 it is interpreted as the fraction of contacts of infected cases that are traced. While this distinction does not matter mathematically it should either be clarified what the interpretation of q is or argued that one can interpret it both ways. (11) is to be the "cumulative size of S q ", then it is missing an integral (from 0 to T ). Indeed setting S 0 = N we see that Equation (11) is the same as the first term in Equation (9g). The same reasoning applies to the Section on quarantine effectiveness in the Appendix (e.g. the right-hand sides of Equations (18) and (19) still depend on t). The authors should check how this affects the simplification presented in Equation (19) (one cannot cancel E t−5 anymore) and the results presented in Figure 4.

If Equation
3 Minor Remarks 1. In Section 3.1 the parameter p Ic is sometimes called p c , this should be unified.
2. Before Equation (17) one actually requires α c S0 N to be big (relative tõ δ and p c ) to arrive at Equation (17); so higher vaccination coverage and lower probability of infection make the approximation worse.